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Nilpotent measures on compact semigroups
Published online by Cambridge University Press: 17 April 2009
Abstract
Let S be a compact semigroup and P(S) the set of probability measures on S. Suppose P(S) has zero θ and define a measure μ ε P(S) nilpotent if μn → θ. It is shown that any measure with support containing that of θ is nilpotent, and the set of nilpotent measures is convex and dense in P(S). A measure μ is called mean-nilpotent if (μ + μ2 + … + μn)/n → θ, and can be characterized in terms of its support.
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- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 12 , Issue 1 , February 1975 , pp. 149 - 153
- Copyright
- Copyright © Australian Mathematical Society 1975
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